Template:Sequence of the Day for June 4

Intended for: June 4, 2013

Timetable

• First draft entered by Alonso del Arte on April 7, 2012 based on remarks by Robert G. Wilson ✓
• Draft reviewed by Daniel Forgues on May 30, 2012 ✓
• Draft to be approved by May 4, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A051762: Decimal expansion of the polygon-circumscribing constant

∏ ∞ n  = 3   1 cos (π / n)

.

8.700036625208...

Here is the geometric interpretation (see circumscribed regular polygons):

• begin with a unit circle;
• circumscribe an equilateral triangle and then circumscribe a circle;
• circumscribe a square and then circumscribe a circle;
• circumscribe a regular pentagon and then circumscribe a circle;
• etc.

The circles have radii which converge to this value.

The reciprocal of the polygon-circumscribing constant gives the polygon-inscribing constant (A085365) (see inscribed regular polygons)

1 / 8.700036625208... = 0.1149420448532...